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Recent questions and answers in Engineering Mathematics
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GATE2019 CE1: 1
Which one of the following is correct? $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=2 $ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})=1$ $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=1$ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})=1$ ... $\lim_{x\rightarrow 0} ( \frac{sin4x}{sin2x})=2$ and $\lim_{x\rightarrow 0} ( \frac{tanx}{x})= \infty$
answered
3 days
ago
in
Calculus
by
Kushagra गुप्ता
(
140
points)
gate2019ce1
calculus
limit
0
votes
0
answers
2
GATE2017 CE219
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
asked
Aug 7, 2019
in
Calculus
by
gatecse
(
3.9k
points)
gate2017ce2
vectorcalculus
divergence
numericalanswers
0
votes
0
answers
3
GATE2017 CE227
Consider the following definite integral: $I= \int_0^1 \frac{(\sin ^{1}x)^2}{\sqrt{1x^2}} dx$. The value of the integral is $\frac{\pi ^3}{24}$ $\frac{\pi ^3}{12}$ $\frac{\pi ^3}{48}$ $\frac{\pi ^3}{64}$
asked
Aug 7, 2019
in
Calculus
by
gatecse
(
3.9k
points)
gate2017ce2
definite
integral
0
votes
0
answers
4
GATE2017 CE228
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to $\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{bmatrix}$ $\begin{bmatrix} 3 & 40 \\ 42 & 8 \end{bmatrix}$ $\begin{bmatrix} 43 & 27 \\ 34 & 50 \end{bmatrix}$ $\begin{bmatrix} 38 & 32 \\ 28 & 56 \end{bmatrix}$
asked
Aug 7, 2019
in
Linear Algebra
by
gatecse
(
3.9k
points)
gate2017ce2
matrix
0
votes
0
answers
5
GATE2017 CE229
Consider the following secondorder differential equation: $y’’ – 4y’+3y =2t 3t^2$. The particular solution of the differential solution equation is $ – 2 2tt^2$ $ – 2tt^2$ $2t3t^2$ $ – 2 2t3 t^2$
asked
Aug 7, 2019
in
Partial Differential Equation (PDE):
by
gatecse
(
3.9k
points)
gate2017ce2
differentialequation
particularsolution
0
votes
2
answers
6
GATE2019 CE2: 43
A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of $6 \: m$ are $1.22, \: 1.67, \: 2.04, \: 2.34, \: 2.14, \: 1.87$, and $1.15 \:m$. The area (in $m^2$, round off to 2 decimal places) bounded by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is ________
answered
Feb 20, 2019
in
Numerical Methods
by
moinkhan
(
140
points)
gate2019ce2
numericalmethods
numericalanswers
+1
vote
0
answers
7
GATE2019 CE1: 2
Consider a twodimensional flow through isotropic soil along $x$ direction and $z$ direction. If $h$ is the hydraulic head, the Laplace's equation of continuity is expressed as $\frac{\partial h}{\partial x}+ \frac{\partial h}{\partial z} = 0$ ...
asked
Feb 14, 2019
in
Partial Differential Equation (PDE):
by
Arjun
(
2.8k
points)
gate2019ce1
laplaceequation
continuity
+1
vote
0
answers
8
GATE2019 CE1: 4
For a small value of $h$, the Taylor series expansion for $f(x+h)$ is $f(x)+h{f}’ (x) + \frac{h^2}{2!}{f}’’(x) + \frac{h^3}{3!}{f}’'’(x)+...\infty $ $f(x)h{f}’ (x) + \frac{h^2}{2!}{f}’’(x)  \frac{h^3}{3!}{f}’'’(x)+...\infty $ $f(x)+h{f}’ (x) + \frac{h^2}{2}{f}’’(x) + \frac{h^3}{3}{f}’'’(x)+...\infty $ $f(x)h{f}’ (x) + \frac{h^2}{2}{f}’’(x)  \frac{h^3}{3}{f}’'’(x)+...\infty $
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
taylorseries
0
votes
0
answers
9
GATE2019 CE1: 23
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flood event (in years, round off to $1$ decimal place is ________
asked
Feb 14, 2019
in
Probability and Statistics
by
Arjun
(
2.8k
points)
gate2019ce1
probability
numericalanswers
0
votes
0
answers
10
GATE2019 CE1: 26
Which one of the following is NOT a correct statement? The function $\sqrt[x]{x}, \: (x>0)$, has the global maxima at $x=e$ The function $\sqrt[x]{x}, \: (x>0)$, has the global minima at $x=e$ The function $x^3$ has neither global minima nor global maxima The function $\mid x \mid$ has the global minima at $x=0$
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce1
maximaminima
0
votes
0
answers
11
GATE2019 CE1: 44
Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round off to $1$ decimal place), is _________
asked
Feb 14, 2019
in
Ordinary Differential Equation (ODE)
by
Arjun
(
2.8k
points)
gate2019ce1
differentialequation
numericalanswers
0
votes
0
answers
12
GATE2019 CE2: 3
The following inequality is true for all $x$ close to $0$. $2\dfrac{x^2}{3} < \dfrac{x \sin x}{1 \cos x} <2$ What is the value of $\underset{x \to 0}{\lim} \dfrac{x \sin x}{1 – \cos x}$? $0$ $1/2$ $1$ $2$
asked
Feb 12, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019ce2
limit
0
votes
0
answers
13
GATE2019 CE2: 26
The probability density function of a continuous random variable distributed uniformly between $x$ and $y$ (for $y>x$) is $\dfrac{1}{xy}$ $\dfrac{1}{yx}$ $xy$ $yx$
asked
Feb 12, 2019
in
Probability and Statistics
by
Arjun
(
2.8k
points)
gate2019ce2
probabilitydensityfunction
randomvariable
uniformdistribution
0
votes
0
answers
14
GATE2019 CE2: 28
An ordinary differential equation is given below; $\left ( \dfrac{dy}{dx} \right ) (x \text{ ln } x)=y$ The solution for the above equation is (Note: $K$ denotes a constant in the options) $y=K x \text{ ln } x$ $y=K x e^x$ $y=K x e^{x}$ $y=K \text{ ln } x$
asked
Feb 12, 2019
in
Ordinary Differential Equation (ODE)
by
Arjun
(
2.8k
points)
gate2019ce2
differentialequation
+1
vote
0
answers
15
GATE2019 CE2: 35
The inverse of the matrix $\begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}$ is $\begin{bmatrix} 10 & 4 & 9 \\ 15 & 4 & 14 \\ 5 & 1 & 6 \end{bmatrix}$ ...
asked
Feb 12, 2019
in
Linear Algebra
by
Arjun
(
2.8k
points)
gate2019ce2
matrixinverse
0
votes
0
answers
16
GATE201624
$X$ and $Y$ are two random independent events. It is known that $P(X)=0.40$ and $P(X \cup Y^C)=0.7$. Which one of the following is the value of $P(X \cup Y)$? $0.7$ $0.5$ $0.4$ $0.3$
asked
Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
(
11.8k
points)
gate2016ce2
0
votes
0
answers
17
GATE201625
What is the value of $\underset{x \rightarrow 0 \\ y \rightarrow 0}{\lim} \frac{xy}{x^2+y^2}$? $1$ $1$ $0$ Limit does not exist
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.8k
points)
gate2016ce2
limit
+1
vote
0
answers
18
GATE2016227
If $f(x)$ and $g(x)$ are two probability density functions, $f(x) = \begin{cases} \frac{x}{a}+1 & :a \leq x < 0 \\ \frac{x}{a}+1 & : 0 \leq x \leq a \\ 0 & :\text{otherwise} \end{cases}$ ... different; Variance of $f(x)$ and $g(x)$ are same Mean of $f(x)$ and $g(x)$ are different; Variance of $f(x)$ and $g(x)$ are different
asked
Mar 28, 2018
in
Probability and Statistics
by
Milicevic3306
(
11.8k
points)
gate2016ce2
probabilitydensityfunction
0
votes
0
answers
19
GATE2016228
The angle of intersection of the curves $x^{2}=4y$ and $y^{2} = 4x$ at point $(0,0)$ is $0^{\circ}$ $30^{\circ}$ $45^{\circ}$ $90^{\circ}$
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.8k
points)
gate2016ce2
0
votes
0
answers
20
GATE2016229
The area between the parabola $x^2=8y$ and the straight line $y=8$ is _______.
asked
Mar 28, 2018
in
Calculus
by
Milicevic3306
(
11.8k
points)
gate2016ce2
definiteintegral
area
numericalanswers
0
votes
0
answers
21
GATE2016230
The quadratic approximation of $f(x)=x^3 – 3x^2 5$ at the point $x=0$ is $3x^2 6x5$ $3x^25$ $3x^2+6x5$ $3x^25$
asked
Mar 28, 2018
in
Numerical Methods
by
Milicevic3306
(
11.8k
points)
gate2016ce2
0
votes
0
answers
22
GATE2017 CE1: 1
The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct? $PQ=I$ but $QP \neq I$ $QP=I$ but $PQ \neq I$ $PQ=I$ and $QP= I$ $PQQP= I$
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
(
11.8k
points)
gate2017ce1
matrixinverse
0
votes
0
answers
23
GATE201524
$\underset{x \to \infty}{\lim} \bigg( 1+ \frac{1}{x} \bigg)^{2x} $ is equal to $e^{2}$ $e$ $1$ $e^2$
asked
Mar 26, 2018
in
Calculus
by
Milicevic3306
(
11.8k
points)
gate2015ce2
0
votes
0
answers
24
GATE2015126
The smallest and largest Eigen values of the following matrix are: $\begin{bmatrix} 3 & 2 & 2 \\ 4 & 4 & 6 \\ 2 & 3 & 5 \end{bmatrix}$ $1.5$ and $2.5$ $0.5$ and $2.5$ $1.0$ and $3.0$ $1.0$ and $2.0$
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
(
11.8k
points)
gate2015ce1
0
votes
0
answers
25
GATE2015128
Consider the following differential equation: $x(y\:dx +x\:dy) \cos \frac{y}{x}=y(x\:dyy\:dx) \sin \frac{y}{x}$ Which of the following is the solution of the above equation ($c$ is an arbitrary constant)? $\frac{x}{y} \cos \frac{y}{x} = c$ $\frac{x}{y} \sin \frac{y}{x} = c$ $xy \cos \frac{y}{x} = c$ $xy \sin \frac{y}{x} = c$
asked
Mar 26, 2018
in
Ordinary Differential Equation (ODE)
by
Milicevic3306
(
11.8k
points)
gate2015ce1
0
votes
1
answer
26
GATE2018 CE1: 1
Which one of the following matrices is singular? $\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$ $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix}$ $\begin{bmatrix} 2 & 4\\ 3 & 6 \end{bmatrix}$ $\begin{bmatrix} 4 & 3\\ 6 & 2 \end{bmatrix}$
answered
Feb 24, 2018
in
Linear Algebra
by
goudarningu
(
360
points)
gate2018ce1
matrix
0
votes
1
answer
27
GATE2018 CE2: 26
The matrix $\begin{pmatrix} 2 & 4 \\ 4 & 2 \end{pmatrix}$ has real eigenvalues and eigenvectors real eigenvalues but complex eigenvectors complex eigenvalues but real eigenvectors complex eigenvalues and eigenvectors
answered
Feb 20, 2018
in
Linear Algebra
by
paiyyawulpuja
(
120
points)
gate2018ce2
matrix
eigenvaluesandeigenvectors
0
votes
1
answer
28
GATE2018 CE1: 37
The solution at $x=1$, $t=1$ of the partial differential equation $\frac{\partial ^2 u}{\partial x^2} = 25 \frac{\partial ^2 u}{\partial t^2}$ subject to initial conditions of $u(0) = 3x$ and $\frac{\partial u}{\partial t}(0) =3$ is _______ $1$ $2$ $4$ $6$
answered
Feb 19, 2018
in
Partial Differential Equation (PDE):
by
praveenkumar_new
(
140
points)
gate2018ce1
partialdifferentialequation
0
votes
1
answer
29
GATE2018 CE1: 38
The solution (up to three decimal places) at $x=1$ of the differential equation $\frac{d^2y}{dx^2} + 2 \frac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ and $\frac{dy}{dx}(0) = 1$ is _____
answered
Feb 18, 2018
in
Ordinary Differential Equation (ODE)
by
pushpendratiwari1011
(
1k
points)
gate2018ce1
differentialequation
numericalanswers
0
votes
1
answer
30
GATE2018 CE2: 20
The quadratic equation $2x^2  3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using NewtonRaphson method is ___
answered
Feb 17, 2018
in
Numerical Methods
by
Pushpendra Tiwari
gate2018ce2
newtonraphsonmethod
numericalanswers
0
votes
0
answers
31
GATE2018 CE2: 28
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & 2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$ $1$ $2$ $3$ $4$
asked
Feb 17, 2018
in
Linear Algebra
by
gatecse
(
3.9k
points)
gate2018ce2
matrixrank
0
votes
0
answers
32
GATE2018 CE2: 19
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is _____
asked
Feb 17, 2018
in
Probability and Statistics
by
gatecse
(
3.9k
points)
gate2018ce2
probability
withoutreplacement
numericalanswers
0
votes
0
answers
33
GATE2018 CE2: 1
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is $x$ $x^2$ $x^{1}$ $x^{2}$
asked
Feb 17, 2018
in
Ordinary Differential Equation (ODE)
by
gatecse
(
3.9k
points)
gate2018ce2
differentialequation
0
votes
0
answers
34
GATE2018 CE1: 26
The value of the integral $\int_0^{\pi} x \cos^2 x \: dx$ is $\pi^2/8$ $\pi^2/4$ $\pi^2/2$ $\pi^2$
asked
Feb 17, 2018
in
Calculus
by
gatecse
(
3.9k
points)
gate2018ce1
integration
0
votes
0
answers
35
GATE2018 CE1: 2
For the given orthogonal matrix Q, $Q = \begin{bmatrix} 3/7 & 2/7 & 6/7 \\ 6/7 & 3/7 & 2/7 \\ 2/7 & 6/7 & 3/7 \end{bmatrix}$ ... $\begin{bmatrix} 3/7 & 6/7 & 2/7 \\ 2/7 & 3/7 & 6/7 \\ 6/7 & 2/7 & 3/7 \end{bmatrix}$
asked
Feb 17, 2018
in
Linear Algebra
by
gatecse
(
3.9k
points)
gate2018ce1
matrixinverse
0
votes
0
answers
36
GATE2018 CE1: 3
At the point $x= 0$, the function $f(x) = x^3$ has local maximum local minimum both local maximum and minimum neither local maximum nor local minimum
asked
Feb 17, 2018
in
Calculus
by
gatecse
(
3.9k
points)
gate2018ce1
maximaminima
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